Vibrations-5.doc

# Calculate the velocity of the drum v and use eqn 6 to

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Calculate the velocity of the drum V , and use eqn-6 to find . Apply again in eqn-5 to find n . Compare it with n-theor . Part Two- Forced Vibration: For the speed of the motor at resonance Nr , find the equivalent angular frequency of the motor . This frequency will be equal to the natural frequency of the system n . Compare it with n-theor . From the value of N at which the second chart has been plotted, find the corresponding angular frequency . 1) Evaluate the frequency ratio r using n-theor , and apply eqn-13 to evaluate MF . 2) From eqn-12 , find Static Y , and from the second chart evaluate Dynamic Y , then apply in eqn-11 to evaluate MF . Compare the results of the two ways. 53

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Mech. Vibrations Lab. Manual, Expr. # 5 Dr. M. Dado, Eng. M. Sha’ban & F. Abu-Farha. VIII- Results: Table-5.3 Data processing analysis Parameter Value M b (kg) I (kg.m 2 ) K (N/m) Table-5.4 Results of the natural frequency by the various methods Method Natural Frequency n (rad/sec) Percent Error ( ) Analytical (E.O.M) Time Measurements Drum Speed Resonance Observation Table-5.5 Magnification Factor MF results Methode-1 (rad/sec) r ( / n) MF Percent Error ( ) Methode-2 Y dynamic (mm) Y static (mm) MF IX- Discussion And Conclusions: 1) What is the meaning of the Static Amplitude of oscillation? In this case, derive the expression of (Y static ) given in eqn-12 ? 54
Mech. Vibrations Lab. Manual, Expr. # 5 Dr. M. Dado, Eng. M. Sha’ban & F. Abu-Farha. 2) Draw the magnification factor MF versus frequency ratio r for the system, for this mode of forced vibrations (Rotating Unbalnce) ? Draw the expected ideal curve for this case, and another one based on your expectations for the real case, showing the deviations from the ideal one. 3) According to your observations and plot in the previous question, did the amplitude of oscillations reach a very high value at resonance? If not, why? 4) In the derivation of the equation of motion for the system, why did not we consider the effect of the gravitational forces (weights of its components) although they have moments about point O ? 5) For a practical system like a machine, suffering from such mode of vibrations, how could you modify its parameters ( or ) , or add other components, in a way that minimises vibrations level? 55

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Mech. Vibrations Lab. Manual, Expr. # 5 Dr. M. Dado, Eng. M. Sha’ban & F. Abu-Farha. 56

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